2020/07/14 by Michel Mandjes, Mandjes, Michel, Jaap Storm +1
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.2007.07339
arxiv created 2020/07/14 · arxiv updated 2020/07/16
In the setting of a recently developed cellular stochastic traffic flow model, it has shown that the joint per-cell vehicle densities, as a function of time, can be accurately approximated by a Gaussian process, which has the attractive feature that its means and (spatial and temporal) covariances can be efficiently evaluated. The present article demonstrates the rich potential of this methodology in the context of road traffic control and transportation network design. To solidly provide empirical backing for the use of a multivariate Gaussian approximation, we rely on a detailed historical dataset that contains traffic flow data. Then, in the remainder of the paper, we provide a sequence of design and control related example questions that can be analyzed using the Gaussian methodology. These cover the following topics: (i) evaluation of stationary performance measures, (ii) route selection, (iii) control of traffic flows, and (iv) performance of traffic networks with arbitrary topology. In discussing the setup, results, and applications of these examples, we stress the appropriateness of our stochastic traffic model over a deterministic counterpart.